Mistake in check in system and *********** staff caused a one week delay in my schedule

I recently visited the US with British Airways using my Taiwanese (TW) passport under the VISA waiver program, with an approved ESTA application. I began my trip to the US on 5th July 2018, from Cape Town-London Heathrow-Philadelphia-Denver. No issues getting out of South Africa to UK using my South African passport, and my TW passport from UK to the US. I was supposed to have a return flight from Denver International Airport-London Heathrow-Cape Town with British Airways on Saturday 28th of July 2018. Flight from Denver was at 19:35, I’ve already checked in on my phone earlier that day and received my mobile boarding pass. Check in at BA counter for bag drop was denied at 17:30. The BA manager (Sonja) stated their system showed a VISA (US, UK, Australia or Canada) is required with a TW passport to transit through UK, even though the official website www.gov.uk stated that it is not required (whether going through immigration/border control or not) as long as a personal ID is listed on the passport (which I have on my passport). Told her I'm just transiting through UK, she called the UK embassy, came back and told me they said a VISA is still required. Sonja then told me she cannot check me in and to contact BA reservations/customer relations. Contacted reservations twice on ********** 9297, kept getting told that checking for VISA requirements is my responsibility (even though I checked and a VISA was not required). I was told to go back to the check in counter to get an extension of 1-2 days whilst acquiring a VISA, and to speak to customer relations. I was given the number ********** 794 by Prashant and was told it will be open on Sunday 7am-2pm EST. I went back to the BA counters around 18:30, all staff has left so I had no choice but to leave the airport. On Sunday 29th July, I called BA customer relations in the morning but it was closed. The automated voice recording says they’re only open Monday-Friday. My cousin in Miami pointed me to the TW embassy in Miami and gave me their contact numbers. On Monday 30th July, I Contacted the TW embassy in Miami ( ********** 917) in the morning and confirmed that a VISA is not required with a TW passport to visit the UK, never mind just transiting. Tried calling BA customer relations as well, lines were busy and gets cut off immediately, got referred to their website by the automated voice recording to contact them via the online form. I went back to the airport, went to BA around 12pm but their counters weren’t open yet. So I tried calling customer relations again, still can't get through. I then called reservations, spoke to Piyush, he was polite and tried to help, I explained my situation to him, and things seemed promising, but in the end he said he couldn't help me reissue a ticket due to discrepancies with the BA counter staff and I need to ask the counter staff to reissue a ticket for me. Around 2-3pm, I stood in line and spoke to Sandy at the BA counters for help. She was rude and unhelpful. She said she was there on Saturday, overheard the conversation with me and Sonja, and she will not help me reissue my ticket without a VISA. I politely told her maybe Sonja made a mistake, confused my passport for a Chinese passport (since Sonja referred to it twice as a Chinese passport, which I tried to correct her. It would’ve been understandable, since a Chinese passport shows People’s Republic of China (PRC) on the front cover, and a TW passport shows Republic of China (ROC)- Taiwan) and told her I’ve checked on www.gov.uk and with the TW embassy and they both say a VISA is not required with my passport. She did not believe me, told me they went through training and they don't make mistakes, and said I need to ask the UK embassy and not the TW embassy. I asked if she could get me the number for the UK embassy, she refused to give me/help me find it, told me to find it online myself “like how I found all the other information”. So I looked online and found a number for the UK embassy ( ********** 500) in Washington USA, called and the automated voice recording just directs me to the www.gov.uk website when I selected the VISA option. Eventually I got through to an operator and told him their site says a VISA is not required with my passport, but BA won't believe me, asked him to speak to BA for me but was told he does not have the authority because he is just the receptionist, but I can trust their website. He told me to call UK consulates NY ( ********** 200) instead, but I couldn't get hold of an operator. Spoke to the manager of the day (I didn’t get her name), she tried to help but says their system still says VISA required even though I showed her the www.gov.uk website, and said she cannot help me. I then called the emergency line for TW embassy in Miami ( ********** 994) and was given the TW embassy emergency line in Denver ( ********** 546), got hold of Shirley Chang and asked her for help. She sent me supporting documents immediately, stating since 2009, TW passport holders do not require a VISA to visit UK as long as the stay is less than 6 months. I went back to speak to the BA manager, asked her if she could speak to Shirley, but she said she is really busy, and explained to me that she can't check me in because if a VISA is required they (BA) will get fined. I told her I am sure I do not need a VISA and I can take on the responsibility of the fine for them, but she said there's nothing she can do because the system will not allow her to check me in, told me to buy a new ticket from another airline (Lufthansa to transit through Frankfurt) and claim a refund from BA. So, feeling hopeless and helpless, I decided to take this advice. I did not have enough balance in my credit card to buy a new ticket, so I had to transfer money into my credit card. I decided that once the money goes in after a couple of days, I will be able to buy a new ticket home, and I filed a claim on the BA website for my flight tickets. I informed my parents of the decision, but they told me to wait for Shirley to go and try help me at the BA counters, if that still doesn’t work then I should buy a new ticket home immediately. So I contacted Shirley and we decided to meet up on Friday 3rd August. Shirley went with me to BA counters around 12pm on Friday 3rd August, their counters only open at 3pm that day, so she tried to find numbers and made a few phone calls to the UK embassy/consulate but also couldn't get hold of someone. Shirley spoke to Sonja around 3-4pm, explained that TW and UK have a VISA waiver program, showed her the supporting documents stating a VISA is not required with my TW passport, but she still does not believe us and said she spoke with the UK embassy and they said a VISA is required. Shirley asked to call the UK embassy herself so Sonja gave her a number (011 44 ********** 920). We got through after a few attempts and spoke to Mr Khan from the UK embassy, we stayed on the line for around 15 minutes for him to get back to us, and he told us that a VISA is not required with my TW passport. Mr Khan couldn't wait on the line while we waited for Sonja (she was briefing her staff). Shirley spoke to Sonja when she was done briefing, explained to her what happened and she called Mr Khan back, she realised there was a mistake and started reissuing a ticket for me for Saturday 4th August. Sonja said BA wanted to charge 1900$ for the reissue, but she waived it for me (even though it wouldn’t have happened in the first place if there wasn’t this mistake on the BA’s system). I told her I'd like an apology from Sandy for being rude and unhelpful on Monday, she said she will get her to apologise to me. But Sandy was busy at the counters, so Sonja told me she will get her to apologise on Saturday when I go to check in. I asked how is BA going to compensate for the delay and the extra expenses caused by this mistake, she told me it was partially my fault for not bringing the supporting documents saying VISA not required and she did not take the responsibility for it (who brings documents to state you don’t need a VISA if a VISA is not required?!). She said BA was going to charge for the ticket reissue already, so they will not compensate, but told me I can try speak to customer relations. She issued me a 9$ meal voucher and a voucher for accommodation at Quality Inn. The ticket reissuing process lasted till 7pm. On Saturday 4th August, the flight was delayed from 19:35 to 22:10, but when I went to check in, everything went fine this time. I asked Sonja about the apology from Sandy, she said she spoke to Sandy, but instead of bringing her to me, I was told to wait in the ticketing line for an apology so I left. I was given another 9$ meal voucher. I saw Sandy when I was boarding, she did not apologise but just said "hi Mr Lin, nice to see you, have a nice trip". The trip went fine with no VISA issues, got back to Cape Town on Monday 6th August around 10am. I am really disappointed with the service from the British Airways staff at the Denver International Airport as well as from their call centre, all the trouble and delay they have caused because of a mistake in their system, the incompetency of their staff, their inability to think out of the box, their unwillingness to take responsibility, and their terrible attitude. Because of this, I was delayed for a week, I am now behind on work, I could’ve gotten suspended/fired. There were extra expenses that incurred which I did not budget for. Where was I supposed to stay for all those days? What about food and transportation expenses to and from the airport in order for me to try fix the ticket issue? What if I did not have enough money to buy another ticket home and get stuck in America? Do they really think 2x 9$ meal vouchers and one night stay at a hotel was enough to make up for this mistake?